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Polarities of Schellhammer planes
-
Steffen Poppitz
and
Markus Stroppel
Published/Copyright:
April 8, 2011
Abstract
We construct polarities for projective planes admitting a group of automorphisms that acts regularly on the complements of an anti-flag in the point and line set. In particular, we determine all polarities of the compact connected planes studied by I. Schellhammer and by P. Sperner. For both classes of planes we solve the conjugacy problem, and determine the set of absolute points for each one of the polarities. Among these polarities we find the first examples of elliptic polarities in non-Moufang compact projective planes.
Received: 2010-08-21
Published Online: 2011-04-08
Published in Print: 2011-April
© de Gruyter 2011
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Articles in the same Issue
- On finite subgroups of compact Lie groups and fundamental groups of Riemannian manifolds
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- Character tables of m-flat association schemes
- Character tables of the association schemes obtained from the finite affine classical groups acting on the sets of maximal totally isotropic flats
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- Polarities of Schellhammer planes
- Substituting compact disks in stable planes
- On the local structure and the homology of CAT(κ) spaces and euclidean buildings
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